Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

Given:

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks.

To do:

We have to find the total number of questions.
Solution:
Let the number of questions answered correctly be $x$ and the number of questions answered incorrectly be $y$.

This implies,

 Total number of questions $=x+y$.

In the first case, 3 marks were awarded for each right answer and $-1$ for every wrong answer. 

According to the question,

$40=3x+(-1)y$

$y=3x-40$.....(i)

In the second case, 4 marks were awarded for each right answer and $-2$ for every wrong answer. 

According to the question,

$50=4x+(-2)y$

$2y=4x-50$

$2y=2(2x-25)$

$y=2x-25$.....(ii)

From (i) and (ii), we get,

$3x-40=2x-25$

$3x-2x=40-25$

$x=15$

This implies,

$y=2(15)-25$

$y=30-25$

$y=5$

$\Rightarrow x+y=15+5=20$

The total number of questions in the test are 20.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

183 Views

Kickstart Your Career

Get certified by completing the course

Get Started